Question

here are some summary statistics for the life spans of two breeds of cats.

breed	mean life span	standard deviation
colorpoint shorthair	$mu = 14$ years	$sigma = 1$ year

fluffy was an abyssinian cat who lived for 13 years, and mittens was a colorpoint shorthair cat who lived for 15 years.

relative to its breed, which cat had a longer lifespan?

Explanation:

Step1: Calculate z - score for Fluffy

The z - score formula is $z=\frac{x-\mu}{\sigma}$. For Fluffy (an Abyssinian cat), $x = 13$ years, $\mu = 12$ years, and $\sigma=1.5$ years. So, $z_{Fluffy}=\frac{13 - 12}{1.5}=\frac{1}{1.5}\approx0.67$.

Step2: Calculate z - score for Mittens

For Mittens (a Colorpoint shorthair cat), $x = 15$ years, $\mu = 14$ years, and $\sigma = 1$ year. So, $z_{Mittens}=\frac{15 - 14}{1}=1$.

Step3: Compare z - scores

Since $z_{Mittens}=1$ and $z_{Fluffy}\approx0.67$, and $1>0.67$.

Answer:

Mittens had a longer lifespan relative to its breed.